Using Dynamic Geometry Software to Engage Students in the Standards for Mathematical Practice: The Case of Ms. Lowe

Background

• 1.

  Ms. Lowe is one of three full time math teachers in the math department at a small Catholic high school and the only Geometry teacher. She teaches two sections of regular Geometry, three sections of honors Geometry, and one section of remedial math for seniors. Although her school does have a few carts of laptops, she finds that her class periods are too short (39 minutes) to make them useful, as she needs to unload and distribute them, have students boot them up and log on (which takes a surprisingly long time), and then log off and reload them all onto the cart again at the end of class. Ms. Lowe has found the computer lab to be much more practical than the laptop carts, but the school’s computer lab is used as a classroom by the business teacher as there is no other classroom space for her in the school. However, the business teacher prefers a regular classroom with fewer distractions (such as computers), so Ms. Lowe has been able to use the computer lab whenever she wishes by swapping classrooms with the business teacher

• 2.

  Ms. Lowe estimates that her 10^th grade honors geometry classes will go to the lab about 12 -15 times over the course of the year. This task takes place in February, midway through the school year. It is one of the final investigations in a GeoGebra intensive unit focusing on properties of triangles. During these lab sessions, the class uses GeoGebra to complete mathematical tasks that Ms. Lowe has written herself in order to supplement their curriculum. She also uses GeoGebra in her classroom, but it is primarily for demonstration purposes; although she does have students come up to the front of the room to use her computer as it is projected onto the dry erase board. The point of taking students to the lab is for them to explore and investigate properties of geometric figures for themselves, instead of just being lectured to and taking notes.

• 3.

  Ms. Lowe values many aspects of mathematics instruction that are typically associated with a reform-oriented style of teaching. She believes that active learning and classroom discourse are important, and she is attentive to the issue of developing students’ ability to reason mathematically and persevere in solving complex problems. However, she also feels somewhat constrained in her ability to fully embrace reformed-oriented instruction due to a number of opposing goals and tensions from various sources. Examples of this include a lack of class time resulting from the need to cover the many topics in her curriculum and having to focus on preparing students for the types of assessments that maximize their chances of college acceptance. Despite these tensions, she does what she can in order to make inquiry-based learning a substantial component in her class, and instructional technologies are one of the means by which she accomplishes this.

• 4.

  Instructional technologies are viewed by Ms. Lowe as a powerful tool for aiding students in exploring important mathematical ideas. She uses technology as a means to support key mathematical practices among students such as conjecturing and justifying. She does, however, worry about providing too much support to students in activities that make use of technology. In particular, she wishes to avoid having technology-based activities simply becoming a set of instructions that students follow without making connections to mathematical ideas and concepts. With this concern in mind, she spends considerable time planning and reflecting on technology tasks in order to determine how best to use technology to support her students’ learning of mathematics.